Friction parameters identification and compensation of LuGre model base on genetic algorithms

Transcription

1 Internatonal Sympoum on Computer & Informat (ISCI 015) Frton parameter dentfaton and ompenaton of LuGre model bae on genet algorthm Yuqn Wen a, Mng Chu b and Hanxu Sun Shool of Automaton, Bejng Unverty of Pot and teleommunaton No10 Xtuheng Road, Hadan Dtrt, Bejng, Chna awyq_bupt@163om Abtrat Aordng to the nterferene of the ervo ytem, a method propoed that dentfy the parameter of LuGre frton model and ompenate the frton torque bae on genet algorthm Frt, etablh the LuGre frton model, on the ba of the model, dentfy the tat parameter and the dynam parameter n turn Seond, ntrodue the frton ompenaton to the feedbak ontrol of the ervo ytem o that to elmnate the nterferene and mprove the ytem trakng auray and robutne Keyword: LuGre frton model; genet algorthm; ervo ytem; frton ompenaton 1 Introduton Frton ext n almot all of the ervo ytem In hgh preon ervo ytem, frton uually ha a trong nonlnear harater and ha mpat on the poton ontrol auray and performane mplaton There are lot of frton model nludng tat model and dynam model Stat model lke Bngham model, Strbek model, Kamopp model and dynam model lke Dahl model, Blman-Sorne model, LuGre model, and o on Whle Genet Algorthm a earhng mehanm that mm the natural bologal evoluton, earhng the optmal oluton n the global ope, an olve LuGre frton model parameter dentfaton problem well LuGre model an well explan rawlng, pre-ldng dplaement, frton memory, rng tat frton Therefore, we adopt th model to analyze In th paper, two apet are dued am at the nterferene problem orgnated from frton: parameter dentfaton and ontrol of frton ompenaton[1] Wth the dentfaton reult, we an ompenate the frton, now that to mprove the tablty and ontrol auray of the ervo ytem 015 The author - Publhed by Atlant Pre 9

2 Frton model The prmary fator n meaurng a frton model whether t an derbe the frton dynam harater neghborng zero peed or not Strbek model handle the trong nonlnear problem well, hene, t an be ondered an deal model A a reult, LuGre model[] apple Strbek whle olve the problem the nonlnear fator affet the frton near zero peed Strbek model an be derbed a: Stat frton, Fm, Ft () > Fm Ff () t = Ft (), Fm < F< Fm Fm, Ft () < Fm (1) Dynam frton, α 1 θ() t Ff () t = F + ( Fm F) e gn θ() t + k vθ () Ft () = J θ () t (3) Where Ft () drvng fore; F m max tat frton; F oulomb frton; k v vou frton torque oeddent; θ () t angular veloty of rotaton;α and α1 mall potve number It hemat dagram a follow, Frton f Stat frton Vou frton Coulomb frton Speed v Fg 1 Strbek frton model dagram The equaton of the frton n ervo ytem an be derbed a, d x m = u F dt (4) 30

3 Among th, m rotatonal nerta, x the dplaement, u preent the ontrol torque and F a frton torque LuGre model bult baed on the average tranformaton of the brtle, preented by z, frton F dz σ 0 x = x z dt g( x ) (5) ( xv / ) ( ) gx ( ) = F+ F F e (6) dz F = σ0z+ σ1 + σx dt (7) Where σ 0 andσ 1 are two dynam parameter; F, F, v, σ are four tat parameter dz When the ytem n table moton, 0 dt = At th tme, F, ( xv / ) F = F ( ) + F F gn( x ) + x (8) From the equaton, we an ee that LuGre frton model ue Strbek model n olvng the problem trong nonlnear near zero peed Meanwhle, t derbe other tat and dynam haratert aurately 3 Parameter dentfaton The dentfaton of LuGre frton model dvded n two tep[3], tat parameter and dynam parameter Frt, we dentfy four tat parameter ung the Strbek urve Seond, dynam parameter dentfaton proeeded baed on the tat parameter dentfaton[4 5] 4 Stat parameter dentfaton The loed-loop ytem move at a grope of nvarable peed{ ω } N = 1, and the orrepondng equene of the ontrol torque are{} u N = 1 From Eq 4, we an ee d x that, when =0, u=f Hene, the two equene above determne the table dt orrepondng relaton between the frton torque and the veloty, whh 31

4 known a the Strbek urve Suppoed the parameter vetor to be dentfed + x = x, x, then, x = FC, FS, v, ( x >0), + x = FC, FS, v, ( x <0) (9) We defne the error of the dentfaton, e( x, x ) = u F( x, x ) ( xv / ) + F + ( F F ) e gn( x ) + xx ( > 0) F( x, x ) = ( xv / ) F + ( F F ) e gn( x ) + xx ( < 0) The objetve funton, N 1 J = e ( x, x ) To dentfy the tat parameter to mnmze the objetve Eq 1 (10) (11) (1) 5 Dynam parameter dentfy When we dentfy the dynam parameter, we ue the output dplaement or aelerate veloty and the output ontrol torque Suppoed the parameter xd = σ0, σ1, we defne the error, e x, t = u t u x, t ( ) ( ) ( ) d d In the equaton, ( ) (13) u x, t u t the ontrol torque of the ervo ytem, ( ) the dentfed output ontrol torque Form Eq 4, we an ee, d x u( xd, t) = F + m dt F = σ z+ σ z + σ x 0 1 d (14) (15) 3

5 σ x 0 z = x z g x ( ) We defne the objetve funton, N 1 J = e ( xd, t) To dentfy the dynam parameter to mnmze the objetve Eq 17 (16) (17) 6 The overall dentty proe PD ontrol Movement ontrol Input torque LuGre frton model jont Low peed move Objetve funton Near zero peed ollaton Objetve funton Data proeng GA dentfaton Speedfrton urve Four tat parameter Two dynam parameter Parameter dentfy F F v 0 Fgure GA dentfaton proe 1 33

6 7 Smulaton and the reult analy Stat frton urve tet and dentfy From Eq 4, we an ee that, nput a ontant peed, we get u=f Eq 11 adapted n pratal ytem frton F = 01503, F = 0631, α = 0019, V = 0051 F = 001, F = 07, α = 009, V = 0051, peed gnal N { x } = = [ ] 10 : 005:10 There are 41 gnal n all Ung PD ontrol to 1 k =, k = 00 When we are trakng the peed gnal, the gnal, whle 00 p d all the gnal orrepond to a trakng reult Fg the trakng urve when the peed one, and the reult ome farly well Fg 3 the trakng error We an tell that the error qute lttle, and approahng to zero Fg 4 the urve error between pratal and dentfed urve When we do the mulaton by ung genet algorthm, determne populaton ze M=100, larget evoluton algebra G=1000 The earhng area of parameter F 0,1, F 0,1, V 0,01, α 0,01 Fg 5 how the are, [ ] [ ] [ ] [ ] pratal urve and the dentfed urve Contrat them, we an ee they are loed The reult deal Identfaton reult are, F = 01503, F = 0631, α = 0019, V = 0051, F 001, F 07, 009, V = = α = = Fg peed trakng 34

7 Fg 3 peed trakng error Fg 4 frton urve error Fg 5 pratal and deal urve 35

8 8 PD ontrol of LuGre model Aordng to Eq 5-7, make J = 1, 0 = 60, 1 = 5, F = 08, F = 034, V = 001, make the y = 01n π t nput gnal ne wave ( ) d Derbe the ontrol algorthm and the ytem by ung Smulnk Choong PD ontrol, k = 0, k = 5, Fg 4 and 5 how the trakng reult p d of poton and peed,t an obvouly fgure out the elng phenomenon Whle n Fg 6-7, we an ee the erou deformaton when the peed ro zero, and trakng dead zone appeared Fg 6 poton trakng Fg 7 peed trakng 36

9 9 Servo ytem frton ompenaton To offet the nfluene brought by frton, we ompenate the frton aordng to the dentfaton reult, ntrodung the ompenaton to ervo ytem, makng t approahng the atual frton nterferene ontnuouly Among the mulaton, tep gnal adopted, hoong LuGre frton model and addng n frton ompenaton Ung real number odng, we determne the ze of ample 30, P = 099, Pm = 010 [1:1: Sze] 001/ Sze Durng dynam dentfyng, uppoed the pratal parameterσ0=03, σ1=015, whle dentfy reultσ0=036, σ1=0147 Fg 9 and10 are the poton and peed trakng of ompenaton ytem We an ee that the peed ro zero and trakng dead zone are dappeared obvouly Fg 9 poton trakng wth ompenaton Fg 10 peed trakng wth ompenaton 37

10 10 Conluon Frton a phenomenon that annot be avoded It an redue the auray of trakng and tablty Through the trakng reult of ervo ytem that ontan frton, we an oberve the effet that brought by frton Ung genet algorthm n dentfyng frton parameter, an remove the effet brought by frton and makng the ytem rapdly repone thu mprove the tablty and trakng auray of the ytem Aknowledgement Th work wa fnanally upported by Projet upported by the Natonal Natural Sene Foundaton of Chna( ), Sentf and tehnologal nnovaton projet of Chnee PLA General Armament Department(ZYX ),the Fundamental Reearh Fund for the Central Unverte(014PTB-00-01) and Natonal Key Ba Reearh Program of Chna (973 Program 013CB733000) Referene [1] Wang X, Wang S, Yao B Adaptve robut ontrol of lnear eletral loadng ytem wth dynam frton ompenaton[c]//advaned Intellgent Mehatron (AIM), 010 IEEE/ASME Internatonal Conferene on IEEE, 010: [] Lee T H, Tan K K, Huang S Adaptve frton ompenaton wth a dynamal frton model[j] Mehatron, IEEE/ASME Tranaton on, 011, 16(1): [3] Lu D P Reearh on parameter dentfaton of frton model for ervo ytem baed on genet algorthm[c]//mahne Learnng and Cybernet, 005 Proeedng of 005 Internatonal Conferene on IEEE, 005, : [4] Nakajma K, Nakajma J, Van Khoa T, et al Identfaton method of nonlnear ytem wth frton baed on Genet Algorthm[C]//Knowledge Aquton and Modelng (KAM), 010 3rd Internatonal Sympoum on IEEE, 010: [5] Lu D P Parameter dentfaton for lugre frton model ung genet algorthm[c]//mahne Learnng and Cybernet, 006 Internatonal Conferene on IEEE, 006: